Dolgachev, Igor; Duncan, Alexander Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2. (English) Zbl 1485.11074 Algebra Number Theory 12, No. 1, 99-130 (2018). Summary: We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective spaces over an arbitrary field of characteristic 2. We use this to obtain a description of the automorphism group of such a variety. As an application, we show that every quartic del Pezzo surface over a perfect field of characteristic 2 has a canonical rational point and, thus, is unirational. Cited in 5 Documents MSC: 11E04 Quadratic forms over general fields 14C21 Pencils, nets, webs in algebraic geometry 14G17 Positive characteristic ground fields in algebraic geometry Keywords:quadratic forms; characteristic 2; quadrics PDFBibTeX XMLCite \textit{I. Dolgachev} and \textit{A. Duncan}, Algebra Number Theory 12, No. 1, 99--130 (2018; Zbl 1485.11074) Full Text: DOI arXiv References: [1] 10.1515/crll.1990.407.75 · Zbl 0693.14015 · doi:10.1515/crll.1990.407.75 [2] 10.2307/2373926 · Zbl 0373.13006 · doi:10.2307/2373926 [3] 10.1007/s002080050235 · Zbl 0913.14015 · doi:10.1007/s002080050235 [4] 10.4171/LEM/58-3-5 · Zbl 1283.13007 · doi:10.4171/LEM/58-3-5 [5] 10.1017/CBO9781139084437 · Zbl 1252.14001 · doi:10.1017/CBO9781139084437 [6] 10.1090/coll/056 · doi:10.1090/coll/056 [7] 10.1007/978-1-4612-1700-8 · doi:10.1007/978-1-4612-1700-8 [8] ; Gauthier, Univ. Politec. Torino Rend. Sem. Mat., 14, 325 (1954-55) [9] 10.1007/BF01467074 · Zbl 0431.14004 · doi:10.1007/BF01467074 [10] 10.1007/978-3-642-56380-5 · doi:10.1007/978-3-642-56380-5 [11] 10.1007/978-1-4612-0853-2 · doi:10.1007/978-1-4612-0853-2 [12] ; Leep, Exposition. Math., 17, 385 (1999) [13] 10.1142/S0219498802000264 · Zbl 1043.11036 · doi:10.1142/S0219498802000264 [14] ; Manin, Uspekhi Mat. Nauk, 41, 43 (1986) [15] 10.4171/LEM/56-1-3 · Zbl 1198.14035 · doi:10.4171/LEM/56-1-3 [16] 10.1007/BF01418967 · Zbl 0337.10015 · doi:10.1007/BF01418967 [17] 10.2140/pjm.1977.69.275 · Zbl 0362.15015 · doi:10.2140/pjm.1977.69.275 [18] ; Weierstrass, Monatsber. Königl. Preuss. Akad. Berlin, 310 (1868) · JFM 01.0054.04 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.